For a multigroup cholera model with indirect transmission, the infection for a susceptible person is almost invariably transmitted by drinking contaminated water in which pathogens, V. cholerae , are present. The basic reproduction number<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msub><mml:mrow><mml:mi>ℛ</mml:mi></mml:mrow><mml:mrow><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>is identified and global dynamics are completely determined by<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:msub><mml:mrow><mml:mi>ℛ</mml:mi></mml:mrow><mml:mrow><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>. It shows that<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mrow><mml:msub><mml:mrow><mml:mi>ℛ</mml:mi></mml:mrow><mml:mrow><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>is a globally threshold parameter in the sense that if it is less than one, the disease-free equilibrium is globally asymptotically stable; whereas if it is larger than one, there is a unique endemic equilibrium which is global asymptotically stable. For the proof of global stability with the disease-free equilibrium, we use the comparison principle; and for the endemic equilibrium we use the classical method of Lyapunov function and the graph-theoretic approach.

Ming-Tao Li

Gui-Quan Sun

Juan Zhang

Zhen Jin

Discrete Dynamics in Nature and Society

自然与社会中的离散动力学的主要目标是促进与自然和社会科学中遇到的复杂系统的离散动力学相关的基础研究和应用研究之间的联系。该杂志旨在促进针对计算机生成解决方案和混沌分析的出版物，特别是数值程序的正确性、混沌同步和控制、离散优化方法以及其他相关主题。该杂志为复杂系统分析领域的科学家和从业者之间的交流提供了一个渠道，并将促进离散动力学方法的开发和使用。

The primary goal of the journal "Discrete Dynamics in Nature and Society" is to foster the connection between fundamental and applied research related to discrete dynamics in complex systems encountered in natural and social sciences. This journal aims to publish works focused on computer-generated solutions and chaos analysis, with particular emphasis on the correctness of numerical programs, chaos synchronization and control, discrete optimization methods, and other related topics. It provides a platform for communication among scientists and practitioners in the field of complex systems analysis and promotes the development and application of discrete dynamics methods.

《Discrete Dynamics in Nature and Society》的主要目标是促进自然科学和社会科学中复杂系统的离散动力学基础研究与应用研究之间的联系。该期刊旨在发表与计算机生成解决方案和混沌分析相关的研究，特别关注数值程序的正确性、混沌同步与控制、离散优化方法及其他相关主题。期刊为复杂系统分析领域的科学家和从业者提供了一个交流的平台，促进离散动力学方法的发展与应用。

Global Dynamic Behavior of a Multigroup Cholera Model with Indirect Transmission

For a multigroup cholera model with indirect transmission, the infection for a susceptible person is almost invariably transmitted by drinking contaminated water in which pathogens, V. cholerae, are present and the basic reproduction number is identified and global dynamics are completely determined by .

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Global Dynamic Behavior of a Multigroup Cholera Model with Indirect Transmission

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